The blue icons in the FamilySearch Family Tree represent historical records that can serve as sources to prove your genealogy. Unlike Hints on sites such as Ancestry and MyHeritage, these are actual historical records, not merely guesses from someone else's family tree. In my experience, about 95% of FamilySearch Hints are for the right people. For the other 5%, we mark them as "Not a Match" and the blue icon disappears.
Not only do the hints provide evidence to support the Family Tree, but they can sometimes identify family members who are missing from the Family Tree. I find censuses especially useful for this purpose, but marriage records may identify the parents of the bride and groom, and various death and burial records may list the immediate family members.
I have usually used the Recommended Tasks or the Landscape view of the Family Tree to find Hints. But three days ago I came across a demonstration by Robert Kehrer, of Family Search. It gives an extremely efficient way of finding source hints across 4 generations of a family at a time. See "Demo: Tips and Tricks for Attaching Records on FamilySearch"
1. Select an ancestor born about 1800
2. View the ancestor's tree
3. Change the Tree View to Descendancy view
4. Click Options to turn off portraits, research suggestions, and temple
5. Select 4 Generations.
Voila! You now have a list of all the ancestor's descendants for 4 generations, with all unattached Hints.
Then it is a simple matter of checking the Hints and attaching those that match. Note that one blue icon may indicate multiple historical records.
When you have finished, you can either choose an ancestor 4 generations further back on that line, or choose an ancestor on a different line. Or you can call it a day, and turn on the items you turned off previously.
Why start at 1800? This is because most historical records start in this time period. Look at the number of generations on that line; sometimes starting about 1850 might be better.
Robert Kehrer is the manager of the Searching and Hinting features in Family Tree.